Average Error: 0.3 → 0.3
Time: 21.0s
Precision: 64
\[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}\]
↓
\[\left(x \cdot 0.5 - y\right) \cdot \left(\left(\sqrt{z \cdot 2} \cdot {\left(\sqrt[3]{e^{t}} \cdot \sqrt[3]{e^{t}}\right)}^{\left(\frac{t}{2}\right)}\right) \cdot {\left(\sqrt[3]{e^{t}}\right)}^{\left(\frac{t}{2}\right)}\right)\]
\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}
↓
\left(x \cdot 0.5 - y\right) \cdot \left(\left(\sqrt{z \cdot 2} \cdot {\left(\sqrt[3]{e^{t}} \cdot \sqrt[3]{e^{t}}\right)}^{\left(\frac{t}{2}\right)}\right) \cdot {\left(\sqrt[3]{e^{t}}\right)}^{\left(\frac{t}{2}\right)}\right)
double f(double x, double y, double z, double t) {
        double r538904 = x;
        double r538905 = 0.5;
        double r538906 = r538904 * r538905;
        double r538907 = y;
        double r538908 = r538906 - r538907;
        double r538909 = z;
        double r538910 = 2.0;
        double r538911 = r538909 * r538910;
        double r538912 = sqrt(r538911);
        double r538913 = r538908 * r538912;
        double r538914 = t;
        double r538915 = r538914 * r538914;
        double r538916 = r538915 / r538910;
        double r538917 = exp(r538916);
        double r538918 = r538913 * r538917;
        return r538918;
}
↓
double f(double x, double y, double z, double t) {
        double r538919 = x;
        double r538920 = 0.5;
        double r538921 = r538919 * r538920;
        double r538922 = y;
        double r538923 = r538921 - r538922;
        double r538924 = z;
        double r538925 = 2.0;
        double r538926 = r538924 * r538925;
        double r538927 = sqrt(r538926);
        double r538928 = t;
        double r538929 = exp(r538928);
        double r538930 = cbrt(r538929);
        double r538931 = r538930 * r538930;
        double r538932 = r538928 / r538925;
        double r538933 = pow(r538931, r538932);
        double r538934 = r538927 * r538933;
        double r538935 = pow(r538930, r538932);
        double r538936 = r538934 * r538935;
        double r538937 = r538923 * r538936;
        return r538937;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.3
Target0.3
Herbie0.3
\[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot {\left(e^{1}\right)}^{\left(\frac{t \cdot t}{2}\right)}\]

Derivation

  1. Initial program 0.3

    \[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}\]
  2. Using strategy rm

  3. Applied *-un-lft-identity0.3

    \[\leadsto \left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{\color{blue}{1 \cdot 2}}}\]

  4. Applied times-frac0.3

    \[\leadsto \left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\color{blue}{\frac{t}{1} \cdot \frac{t}{2}}}\]

  5. Applied exp-prod0.3

    \[\leadsto \left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot \color{blue}{{\left(e^{\frac{t}{1}}\right)}^{\left(\frac{t}{2}\right)}}\]

  6. Simplified0.3

    \[\leadsto \left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot {\color{blue}{\left(e^{t}\right)}}^{\left(\frac{t}{2}\right)}\]
  7. Using strategy rm

  8. Applied associate-*l*0.3

    \[\leadsto \color{blue}{\left(x \cdot 0.5 - y\right) \cdot \left(\sqrt{z \cdot 2} \cdot {\left(e^{t}\right)}^{\left(\frac{t}{2}\right)}\right)}\]
  9. Using strategy rm

  10. Applied add-cube-cbrt0.3

    \[\leadsto \left(x \cdot 0.5 - y\right) \cdot \left(\sqrt{z \cdot 2} \cdot {\color{blue}{\left(\left(\sqrt[3]{e^{t}} \cdot \sqrt[3]{e^{t}}\right) \cdot \sqrt[3]{e^{t}}\right)}}^{\left(\frac{t}{2}\right)}\right)\]

  11. Applied unpow-prod-down0.3

    \[\leadsto \left(x \cdot 0.5 - y\right) \cdot \left(\sqrt{z \cdot 2} \cdot \color{blue}{\left({\left(\sqrt[3]{e^{t}} \cdot \sqrt[3]{e^{t}}\right)}^{\left(\frac{t}{2}\right)} \cdot {\left(\sqrt[3]{e^{t}}\right)}^{\left(\frac{t}{2}\right)}\right)}\right)\]

  12. Applied associate-*r*0.3

    \[\leadsto \left(x \cdot 0.5 - y\right) \cdot \color{blue}{\left(\left(\sqrt{z \cdot 2} \cdot {\left(\sqrt[3]{e^{t}} \cdot \sqrt[3]{e^{t}}\right)}^{\left(\frac{t}{2}\right)}\right) \cdot {\left(\sqrt[3]{e^{t}}\right)}^{\left(\frac{t}{2}\right)}\right)}\]

  13. Final simplification0.3

    \[\leadsto \left(x \cdot 0.5 - y\right) \cdot \left(\left(\sqrt{z \cdot 2} \cdot {\left(\sqrt[3]{e^{t}} \cdot \sqrt[3]{e^{t}}\right)}^{\left(\frac{t}{2}\right)}\right) \cdot {\left(\sqrt[3]{e^{t}}\right)}^{\left(\frac{t}{2}\right)}\right)\]

Reproduce

herbie shell --seed 2019323 
(FPCore (x y z t)
  :name "Data.Number.Erf:$cinvnormcdf from erf-2.0.0.0, A"
  :precision binary64

  :herbie-target
  (* (* (- (* x 0.5) y) (sqrt (* z 2))) (pow (exp 1) (/ (* t t) 2)))

  (* (* (- (* x 0.5) y) (sqrt (* z 2))) (exp (/ (* t t) 2))))